title: Molecular radiotherapy: the NUKFIT software for calculating the time-integrated activity coefficient.
abstract: OBJECTIVE
  Calculation of the time-integrated activity coefficient (residence time) is a crucial step in dosimetry for molecular radiotherapy. However, available software is deficient in that it is either not tailored for the use in molecular radiotherapy and/or does not include all required estimation methods. The aim of this work was therefore the development and programming of an algorithm which allows for an objective and reproducible determination of the time-integrated activity coefficient and its standard error.
  
  
  METHODS
  The algorithm includes the selection of a set of fitting functions from predefined sums of exponentials and the choice of an error model for the used data. To estimate the values of the adjustable parameters an objective function, depending on the data, the parameters of the error model, the fitting function and (if required and available) Bayesian information, is minimized. To increase reproducibility and user-friendliness the starting values are automatically determined using a combination of curve stripping and random search. Visual inspection, the coefficient of determination, the standard error of the fitted parameters, and the correlation matrix are provided to evaluate the quality of the fit. The functions which are most supported by the data are determined using the corrected Akaike information criterion. The time-integrated activity coefficient is estimated by analytically integrating the fitted functions. Its standard error is determined assuming Gaussian error propagation. The software was implemented using MATLAB.
  
  
  RESULTS
  To validate the proper implementation of the objective function and the fit functions, the results of NUKFIT and SAAM numerical, a commercially available software tool, were compared. The automatic search for starting values was successfully tested for reproducibility. The quality criteria applied in conjunction with the Akaike information criterion allowed the selection of suitable functions. Function fit parameters and their standard error estimated by using SAAM numerical and NUKFIT showed differences of <1%. The differences for the time-integrated activity coefficients were also <1% (standard error between 0.4% and 3%). In general, the application of the software is user-friendly and the results are mathematically correct and reproducible. An application of NUKFIT is presented for three different clinical examples.
  
  
  CONCLUSIONS
  The software tool with its underlying methodology can be employed to objectively and reproducibly estimate the time integrated activity coefficient and its standard error for most time activity data in molecular radiotherapy.
authors.affiliation: Klinik für Nuklearmedizin, Universität Ulm, Ulm 89081, Germany.
authors.forename: P
authors.initials: P
authors.lastname: Kletting
authors.forename: S
authors.initials: S
authors.lastname: Schimmel
authors.forename: H A
authors.initials: HA
authors.lastname: Kestler
authors.forename: H
authors.initials: H
authors.lastname: Hänscheid
authors.forename: M
authors.initials: M
authors.lastname: Luster
authors.forename: M
authors.initials: M
authors.lastname: Fernández
authors.forename: J H
authors.initials: JH
authors.lastname: Bröer
authors.forename: D
authors.initials: D
authors.lastname: Nosske
authors.forename: M
authors.initials: M
authors.lastname: Lassmann
authors.forename: G
authors.initials: G
authors.lastname: Glatting
mesh_terms: D011881:Radiotherapy, Computer-Assisted / Q000379:methods*; D012984:Software; D013997:Time Factors